1. Probing the gluon Wigner distribution in diffractive dijet production
Yoshitaka Hatta
(Yukawa Institute, Kyoto U.)
YH, Xiao, Yuan, PRL 116 (2016)
Hagiwara, YH, Ueda, PRD 94 (2016)
YH, Nakagawa, Yuan, Zhao,
　　 Hagiwara, YH, Pasechnik, Tasevsky , Teryaev, work in progress

2. Nucleon tomography 3D tomography
Partons are characterized by not only the longitudinal momentum fraction ,
but also by the transverse momentum (TMD)
and impact parameter (GPD)
3D tomography

3. 5D tomography: Wigner distribution— the “mother distribution”
Belitsky, Ji, Yuan (2003);
TMD
GPD
PDF
Form factor
charge

4. 5D tomography: GTMD and Husimi
Meissner, Metz, Schlegel (2009)
Hagiwara, YH (2015)
Gaussian smearing in k, b
PDF
Form factor
charge
TMD
GPD

5. Wigner/Husimi/GTMD model calculations, 1-loop calculations, evolution...
Lorce, Pasquini
Liu, Ma
Mukherjee, Nair, Ojha
Courtoy, Goldstein, Hernandez, Liuti, Rajan
Hagiwara, YH、
Echevarria, Idilbi, Kanazawa, Lorce,
Metz, Pasquini, Schlegel
Gutsche, Lyubovitskij, Schmidt
…..
Wigner
Husimi
GTMD

6. Parton orbital angular momentum
Nucleon spin decomposition
Quarks’ helicity
Gluons’ helicity
Canonical Orbital angular momentum
Lorce, Pasquini, (2011);
YH (2011)

7. Wigner distribution: Is it measurable?
In quantum optics, yes!
What about in QCD? Go to small-x!

8. Dipole gluon Wigner distribution at small-x
YH, Xiao, Yuan (2016)
Approximate
``Dipole S-matrix”
Find a process sensitive to both and .

9. Diffractive vector meson production
A phase factor needed
YH, Xiao, Yuan
One can study the dependence
on (Munier, Stasto, Mueller, 2001)
but not on

10. Diffractive dijet production
Altinoluk, Armesto, Beuf, Rezaeian (2015)
YH, Xiao, Yuan (2016)
Jet 1
Jet 2
Proton recoil momentum
Dijet relative momentum
Fourier transform of
　dominated by
for small-

11. `Elliptic’ Wigner distribution
correlation between and expected at small-x
Small in magnitude (a few percent effect)
Distinct functional dependence on
Hagiwara, YH, Ueda (2016)
Elliptic Wigner also relevant to:
`elliptic flow’ in pA and pp collisions
gluon transversity GPD and correlation in DVCS
correlation in quasielastic scattering
Hagiwara, YH, Xiao, Yuan (2017)
YH, Xiao, Yuan (2017)
Zhou (2016)

12. Computing Wigner from BK
Hagiwara, YH, Ueda (2016)
Solve Balitsky-Kovchegov with b-dependence.
Gubser (2011)
Assume that a SO(3) subgroup of conformal group survives
Traveling wave
(geometric scaling)
No traveling wave!

13. Measuring Wigner in ultra-peripheral pA collisions
Hagiwara, YH, Pasechnik, Tasevsky, Teryaev, in progress
preferably small
Use the Weiszacker-Williams photons
with in UPC!
YH, Xiao, Yuan (2016)
photon flux

14. Gluon orbital angular momentum
Challenge: Can we measure OAM?
OAM parton distribution
Look at the component
Then
Find a process sensitive to

15. - Longitudinal single spin asymmetry in diffractive dijet production 2
YH, Nakagawa, Yuan, Zhao (2016)
Yong Zhao, talk on Thursday 2 2 -
Vanishes in the eikonal approximation. Go to next-to-eikonal.
cf. Altinoluk, Armeso, Beuf, Martinez, Salgado (2014)

16. The asymmetry
Odderon!
Conjecture : at small-x

17. Conclusions
Gluon Wigner distribution in QCD measurable in diffractive dijet production in DIS and UPC
Elliptic Wigner responsible for correlations in dijet, , DVCS,…
OAM at small-x also accessible.
Unexpected connection between and
What about quark Wigner? Bhattacharya, Metz, Zhou